Chern-Simons function

Question

The Chern-Simons function on the space of connections, mod the gauge transformations, on a 3-manifold can be defined by an integral. I study mathematics as profession, so I want to know what is the significance (i.e. meaning, intuition, etc) of space of connections in physics. It makes sense mathematically, it is just a manifold. But what is this space really and what does integration on it mean in physics?

This post imported from StackExchange Physics at 2015-09-23 09:29 (UTC), posted by SE-user nikita

Comments

The space of connections (quotiented by gauge orbits) is the integration domain of the path integral, hence your question reduces down to the physical interpretation of the path integral. For that see for example this

This post imported from StackExchange Physics at 2015-09-23 09:30 (UTC), posted by SE-user bechira